Parameter Estimation for the Double Pareto Distribution

Abstract

<B>Problem statement:</B> The double Pareto distribution appeared most often as model for variety of fields, including archaeology, biology, economics, environmental science, finance and physics. The distribution exhibits Paretian power-law behavior in both tails. The family of double Pareto distributions has recently been proposed for modeling growth rates such as annual gross domestic product, stock prices, foreign currency exchange rates and company sizes. In this study, I develop parameter estimates for the double Pareto distribution that are easy to compute. I compare the performance of the maximum likelihood estimate with Bayesian and the method of moments estimates. <B>Approach:</B> This study contracted with maximum likelihood, the method of moments and Bayesian using Jeffrey’s prior and the extension of Jeffrey’s prior information. The comparisons are made on the performance of these estimators with respect to the Mean Squared Error (MSE) for small, moderate and large samples and for some values of the scale and the extension of Jeffrey’s prior parameters using the simulation techniques. <B>Results:</B> It turns out that the maximum likelihood method and Bayesian method with Jeffrey’s prior result in smaller MSE compared to others in all cases. <B>Conclusion:</B> Based on the results of the simulation, the maximum likelihood method and Bayesian method with Jeffrey’s prior are found to be the best with respect to MSE

Shape Factor Asymptotic Analysis II

“…PDF with Equation (39) form is called Double Pareto distribution (DP) in Reed (2001), which is a very active distribution in contemporary researches. Reed (2003), Reed and Jorgensen (2004), Mitzenmacher (2004), Ribeiro et al (2010), Faris (2011), Okamota (2013, Shin et al (2015), Toda (2017), Pfitzinger et al (2018), andShriram (2018) are some of the references for DP with topics ranging from theory to multitude applications. The skewness and kurtosis of DP when m>0 and n>0 are in .…”

Parametric inference of non-informative censored time-to-event data

“…Example 1 In this section, we analyse one data set to obtain the parameter estimates and their standard errors in order to compare the estimators assumed in this paper. The data below are obtained from Lawless 20 about remission times, in weeks, for a group of 30 patients with leukaemia who received similar treatment (asterisks denote censoring times): 1,1,2,4,4,6,6,6,7,8,9,9,10,12,13,14,18,19,24,26,29, 31*, 42, 45*, 50*, 57, 60, 71*, 85*, 91. Using the iterative procedure suggested from the beginning of this paper, the MLEs ofθ andp can be obtained as 28.27991 and 0.99201, respectively, with their corresponding standard errors as 1.56748 and 0.02386.…”